Retrieving "Incompressible Flow" from the archives

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1. Vortex

   Linked via "incompressible flow"

   $$\Gamma = \oint_C \mathbf{v} \cdot d\mathbf{l}$$
   For an ideal, incompressible flow, two-dimensional flow (such as potential flow), the velocity field $\mathbf{v}$ at a distance $r$ from the vortex center is inversely proportional to $r$: $v_\theta = \frac{\Gamma}{2\pi r}$. Integrating this velocity yields the characteristic logarithmic velocity profile.
   However, real-world vortices, particularly those exhibiting turbulence, adhere more closely to the [Rankine combined vortex model](/entries/rankine-combine…